Types of Energy

Why This Matters

Energy is the currency of physics—every problem you solve on the AP exam ultimately comes down to tracking where energy comes from, where it goes, and how it transforms. You're being tested on your ability to recognize energy conservation, work-energy relationships, and energy transfer mechanisms. These concepts appear everywhere: from simple projectile motion to complex thermodynamic systems.

The key insight is that energy is never created or destroyed—it just changes form. When you see a roller coaster climbing a hill, a spring launching a ball, or a circuit powering a light bulb, you're watching energy transform from one type to another. Don't just memorize definitions—know what type of energy is present at each stage of a process and how to calculate the conversions between them.

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Mechanical Energy: The Foundation of Motion Problems

Mechanical energy combines the energy of motion and position into one powerful framework. In isolated systems with no friction or external forces, total mechanical energy stays constant—this principle drives most of your kinematics and dynamics problems.

Kinetic Energy

• Energy of motion calculated as $KE = \frac{1}{2}mv^2$—note that velocity is squared, so doubling speed quadruples kinetic energy
• Scalar quantity that depends on the reference frame—always positive regardless of direction
• Central to collision analysis where you'll compare KE before and after to determine if collisions are elastic or inelastic

Gravitational Potential Energy

• Position-based energy calculated as $PE_g = mgh$—the height $h$ is always measured relative to a chosen reference point
• Converts to kinetic energy as objects fall, with the sum $KE + PE$ remaining constant in free fall
• Reference point is arbitrary but must stay consistent throughout a problem—exam questions often test this understanding

Elastic Potential Energy

• Stored in deformed materials like springs, calculated as $PE_e = \frac{1}{2}kx^2$—where $k$ is the spring constant and $x$ is displacement from equilibrium
• Quadratic relationship means doubling compression quadruples stored energy—similar pattern to kinetic energy
• Drives oscillatory motion in spring-mass systems and appears frequently in simple harmonic motion problems

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Energy Stored in Matter

Some energy forms are locked within the structure of matter itself—in molecular bonds, atomic nuclei, or the random motion of particles. These forms often appear in energy transformation problems where mechanical energy alone can't explain the system's behavior.

Chemical Energy

• Stored in molecular bonds and released or absorbed during reactions—think batteries, food, and fuel
• Converts to other forms such as thermal energy (combustion) or electrical energy (batteries)
• Conservation still applies—the energy released equals the difference in bond energies between reactants and products

Nuclear Energy

• Released from changes in atomic nuclei through fission (splitting heavy atoms) or fusion (combining light atoms)
• Mass-energy equivalence applies: $E = mc^2$ explains why tiny mass changes release enormous energy
• Binding energy per nucleon determines whether fusion or fission is favorable—iron-56 is the most stable nucleus

Thermal Energy

• Internal kinetic energy of particles directly related to temperature—faster particles mean higher temperature
• Transferred via conduction, convection, and radiation—these mechanisms appear in thermodynamics problems
• Often represents "lost" mechanical energy due to friction—when KE seems to disappear, it's usually becoming thermal energy

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Energy in Fields and Waves

Energy doesn't require matter to exist—it can propagate through fields and travel as waves. These forms are essential for understanding circuits, optics, and modern physics.

Electrical Energy

• Associated with electric charge separation and calculated using $PE_e = qV$ where $q$ is charge and $V$ is electric potential
• Powers circuits where energy transforms from electrical to thermal (resistors), mechanical (motors), or light (LEDs)
• Work done by electric fields equals $W = q\Delta V$—this connects to potential difference in circuit analysis

Electromagnetic Energy

• Carried by EM waves including radio, visible light, and X-rays—all travel at $c = 3 \times 10^8 \text{ m/s}$ in vacuum
• Photon energy calculated as $E = hf$ where $h$ is Planck's constant and $f$ is frequency
• Intensity decreases with distance following the inverse square law—crucial for radiation and optics problems

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Mechanical Energy as a System Property

Understanding how kinetic and potential energy combine gives you a powerful problem-solving tool. The mechanical energy framework lets you skip complicated force analysis and jump straight to energy conservation.

Mechanical Energy (Total)

• Sum of kinetic and potential energies: $E_{mech} = KE + PE_g + PE_e$—includes all forms relevant to the system
• Conserved when only conservative forces act—gravity and springs are conservative; friction and air resistance are not
• Work by non-conservative forces equals the change in mechanical energy: $W_{nc} = \Delta E_{mech}$—this is how you handle friction

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Self-Check Questions

1. A ball is thrown upward. At what point is its mechanical energy entirely kinetic? Entirely gravitational potential? How do you know the total stays constant?

2. Compare elastic potential energy and gravitational potential energy: what mathematical similarity do they share with kinetic energy, and why does this matter for energy conservation problems?

3. If a system loses mechanical energy due to friction, where does that energy go? How would you account for this in a calculation?

4. An FRQ shows a spring launching a ball vertically. What three energy types are involved, and at what positions would you evaluate each?

5. Why does nuclear energy release so much more energy per kilogram than chemical energy, even though both involve stored energy in matter? What equation explains this difference?